Question

list the angles of the triangle in order from smallest to largest.
△abc, where cb = 7, ab = 8, and ac = 3
choose the correct order of the angles from smallest to largest.
a. ∠a, ∠b, ∠c
b. ∠c, ∠a, ∠b
c. ∠b, ∠a, ∠c
d. ∠b, ∠c, ∠a
e. ∠a, ∠c, ∠b
f. ∠c, ∠b, ∠a

Explanation:

Step1: Recall the triangle side - angle relationship

In a triangle, the larger the side, the larger the angle opposite it.

Step2: Order the sides

Given \(CB = 7\), \(AB = 8\), and \(AC = 3\). Order of sides from smallest to largest: \(AC\lt CB\lt AB\).

Step3: Determine the angles opposite the sides

Angle opposite \(AC\) is \(\angle B\), angle opposite \(CB\) is \(\angle A\), angle opposite \(AB\) is \(\angle C\).

Step4: Order the angles

Since \(AC\lt CB\lt AB\), then \(\angle B\lt\angle C\lt\angle A\) (by the side - angle relationship in a triangle).

Answer:

D. $\angle B$, $\angle C$, $\angle A$